Spreading speeds of a nonlocal diffusion model with free boundaries in the time almost periodic media

TL;DR

This paper studies the spreading behavior of a nonlocal diffusion model with free boundaries in time almost periodic media, deriving the asymptotic spreading speed under certain conditions.

Contribution

It introduces a novel approach to determine the unique asymptotic spreading speed in a nonlocal diffusion model within time almost periodic environments.

Findings

Established the long-term spreading dynamics.

Derived the asymptotic spreading speed using positive time almost periodic functions.

Identified threshold conditions for the kernel function.

Abstract

In this paper, we mainly investigate the spreading dynamics of a nonlocal diffusion KPP model with free boundaries which is firstly explored in time almost periodic media. As the spreading occurs, the long-run dynamics are obtained. Especially, when the threshold condition for the kernel function is satisfied, applying the novel positive time almost periodic function, we accurately express the unique asymptotic spreading speed of the free boundary problem.